Constraints on Density and Shear Velocity Contrasts at Inner Core Boundary

Aimin Cao and Barbara Romanowicz

Introduction

Density and shear velocity contrasts at the Inner Core Boundary (ICB) likely play a significant role in the character of the Earth's geodynamo and the evolution of the inner core. While studies of geodynamo have been made remarkable progress in the past decades (e.g., Hewitt et al., 1975; Backus, 1975; Gubbins, 1977; Loper, 1978; Mollett, 1984; Buffet et al., 1996; Labrosse et al., 1997; Stacey and Stacey, 1999), the density and shear velocity contrasts at ICB are still controversial issues.

So far there are basically three distinct ways to constrain the density and shear velocity contrasts at the ICB. The first one is using the normal modes which are sensitive to the inner core structure (Gilbert et al., 1973; Gilbert and Dziewonski, 1975; Masters, 1979). This technique suggested a density jump of 0.5-0.6 $gcm^{-3}$ and a shear velocity jump of 3.45 $kms^{-1}$ at the ICB.

The second one is using the body wave amplitude and waveform modeling of PKP and PKiKP. This technique suggested a density jump of 0-1.2 $gcm^{-3}$ (Hage, 1983) and shear velocity jumps of 2.5-3.0 $kms^{-1}$ (Hage, 1983), 2-4 $kms^{-1}$ (Cummins and Johnson, 1988) at the ICB.

The third one is using body wave amplitude ratio of PKiKP to PcP. Bolt and Qamar (1970) first demonstrated this technique and estimated a maximum density jump of 1.8 $gcm^{-3}$ at the ICB. Souriau and Souriau (1989) further constrained the density jump in the range of 1.35-1.6 $gcm^{-3}$. The latest estimation using this method was conducted by Shearer and Masters (1990) who suggested the density jump to be less than 1.0 $gcm^{-3}$ and shear velocity jump to be greater than 2.5 $kms^{-1}$ at the ICB.

Compared with the results derived from normal modes, the constraint on the density contrast from body waves is much more rough and scattered. Therefore, right now the simulations of geodynamo usually refer to the density contrast derived from normal modes.

Nevertheless, a recent geodynamo study (Stacey and Stacey,1999) explicitly pointed out that the inner core would not have existed 2 billion years ago if based on the density contrast at the ICB in the current Earth models. This is obviously against the paleomagnetic evidence, which shows that the Earth has sustained a magnetic field for at least 3 billion years (McElhinny and Senanayake, 1980). And the magnetic field is induced by the geodynamo that is powered by energy mainly associated with the cooling and gradual solidification of the core (Gubbins, 1977; Loper, 1978,1991; Gubbins et al., 1979). Fortunately this conflict can be readily settled if the density contrast at the ICB is somewhat higher than the assumed value in the seismic inner core models, because the energies of the geodynamo are proportional to the assumed density contrast (Stacey and Stacey, 1999). In this study, we try to constrain the density and shear velocity contrasts at the ICB by means of body wave PKiKP/PcP amplitude ratio taking advantage of the availability of recent high quality broadband data.

Data, Method, and Results

We systematically downloaded all of the broadband vertical component data in the epicentral distance range between $10^o$ and $70^o$, from 1990 to 1999, stored in IRIS Data Management Center (DMC). Before searching for PKiKP and PcP arrivals, the event original time and hypocentral parameters were modified with the relocated earthquake catalog (Engdahl et al., 1998) at first, and then theoretical arrivals (PcP, PKiKP, P, pP, PP, PPP, S, SS, and ScS) were labeled with reference to ak135 model (Kennett et al., 1995) after the corrections for ellipticity. The additional 7 theoretical arrivals are the most potential interfering sources for PcP and PKiKP phases. Then the seismograms were filtered in band pass 0.7-3 Hz (PKiKP phase is typically with 1 Hz frequency).

Figure 36.1: A Quality A example with very clear PKiKP and PcP phases. Dashed lines are the theoretical arrivals. The PKiKP/PcP ratio is 0.071.
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The picking quality is classified into three categories A, A-, and B. Quality A means there are very clear PKiKP and PcP phases within 5 seconds of their theoretical arrivals, there is no other theoretical arrival 20 seconds preceding the identified PKiKP or PcP phases (unless the potential interfering arrival can be verified from nodal plane), and the average peak-to-peak signal-to-noise ratio is less than 40$\%$. Quality A- means there are clear PKiKP and PcP phase within 5 seconds of their theoretical arrivals, there is no other theoretical arrival 20 seconds preceding the identified PKiKP or PcP, and the average peak-to-peak signal-to-noise ratio is larger than 40$\%$. Quality B means there is no observable PKiKP phase within 5 seconds of its theoretical arrival, but there is also no any other theoretical arrival 50 seconds preceding the theoretical PKiKP arrival, and PcP phase is very clear within 5 seconds of its theoretical arrival.

Based on above criteria, we collected 5, 16, and 62 Quality A, A-, and B data, respectively. One of the Quality A data is shown in Figure 36.1. The final measurements of PKiKP/PcP ratios were conducted directly with the peak-to-peak amplitudes of the identified PKiKP and PcP phases for Quality A and Quality A- data. For Quality B data, the maximum peak-to-peak amplitude 5 seconds around PKiKP theoretical arrival was read as the upper limit of the PKiKP amplitude (Figure 36.2).




Figure 36.2: Measurements of PKiKP/PcP ratios. The stars denote the Quality A data; the grey squares denote the Quality A- data; and the open dots are the Quality B data. The curves are the theoretical functions of PKiKP/PcP with respect to PREM. Other open symbols are data from previous studies. Our current estimates favor a somewhat larger density jump at the ICB than for PREM
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\epsfig{file=aimin_03_02.eps, width=8cm, bbllx=125,bblly=210,bburx=480,bbury=553}\end{center}\end{figure}

Acknowledgements

We are grateful to the IRIS Data Management Center (DMC) and the network or station operators who contributed data to the DMC.

References

Backus, G.E., Gross thermodynamics of heat engines in deep interior of Earth, Nat. Acad. Sci. USA, 72, 1555-1558, 1975.

Bolt, B.A., and A. Qamar, Upper bound to the density jump at the boundary of the Earth's inner core, Nature, 228, 148-150, 1970.

Buffet, B.A., H.E. Huppert, J.R. Lister, and A.W. Woods, On the thermal evolution of the Earth's core, J. Geophys. Res., 101, 7989-8006, 1996.

Cummins, P., and L.R. Johnson, Short-period body wave constraints of properties of the Earth's inner core boundary, J. Geophys. Res., 93, 9058-9074, 1988.

Gilbert, F., A.M. Dziewonski, and J.N. Brune, An informative solution to a seismological inverse problem, Proc. Natl. Acad. Sci., 70, 1410-1413, 1973.

Gilbert, F., and A.M. Dziewonski, An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Phil. Trans. R. Soc. Lond., A278, 187-269, 1975.

Gubbins, D., Energetics of the Earth's core, J. Geophys., 43, 453-464, 1977.

Hage, H., Velocity constraints for the inner core inferred from long-period PKP amplitudes, Phys. Earth Planet. Inter., 31, 171-185, 1983.

Hewitt, J.M., D.P. McKenzie, and N.O. Weiss, Dissipative heating in convective flows, J. Fluid Mech., 68, 721-738, 1975.

Labrosse, S., J.P. Poirier, and J.L. LeMouel, On cooling of the Earth's core, Phys. Earth Planet. Int., 99, 1-17, 1997.

Loper, D.E., The gravitationally powered dynamo, Geophys. J. R. Astron. Soc., 54, 389-404, 1978.

Masters, G., Observational constraints on the chemical and thermal structure of the earth's deep interior. Geophys. J. R. Astron. Soc., 57, 507-534, 1979.

Mollett, S., Thermal and magnetic constraints on the cooling of the Earth, Geophys. J. R. Astron. Soc., 76, 653-666, 1984.

Souriau, A., and M. Souriau, Ellipticity and density at the inner core boundary from sub-critical PKiKP and PcP data, Geophys. J. Int., 98, 39-54, 1989.

Stacey, F.D., and C.H.B. Stacey, Gravitational energy of core evolution: implications for thermal history and geodynamo power, Phys. Earth Planet. Int., 110, 83-93, 1999.

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